Path rendering is a style of resolution-independent two dimensional (2D) rendering, often called “vector graphics,” that is the basis for a number of important rendering standards. These rendering standards include PostScript, Java 2D, Quartz 2D, OpenVG, PDF, TrueType fonts, OpenType fonts and PostScript fonts, as well as drawings in Office file formats including PowerPoint and Adobe Illustrator illustrations, for example. Additionally, Internet applications include Scalable Vector Graphics (SVG), Silverlight and Adobe Flash for interactive web experiences and XML Paper Specification (XPS).
A path may be rendered into a frame buffer by first determining the coverage of the path in a stencil buffer and subsequently covering the stenciled region with bounding geometry that shades the covered pixels. Paths may include cubic Bezier curve segments and determining the coverage of filled cubic Bezier segments is a mathematically involved process. In a current practice of setting up texture coordinates, the cubic equation may be determined to be one of three curve types by classifying its roots wherein coefficients are themselves 3×3 matrix determinants of the original cubic equation control points. Improvements in evaluating filled cubic Bezier segments for rendering would be beneficial to the art.